\chapter{Conclusions}
The study has thoroughly analyzed the dynamics of weather regimes during the winter season in the North Atlantic-European zone. Starting from raw meteorological data, we built an historical dataset of daily weather regimes, based on a more sophisticated modeling assumption. Consequently, it has allowed us to perform a finer quantification both in the meteorological and energy domain, evidencing some neat trends under the different regimes' distributions. Such knowledge entails an instrument to better address and interpret weather impact in the context of energy markets, clearly representing one of the ``fundamentals'' used in the trading strategies.

As a last step, we have leveraged a new product in the weather community, possibly opening new future scenarios in the forecasting domain. The span of medium-term forecasts, combined with the predictability of the regimes configurations, clearly play a pivotal role in determining a window of opportunity, where some trends can be spotted up to 4-5 weeks with anticipation. Of course, the current limitation of the product, both in terms of accuracy and recent availability, are two key limiting factors for a continuous deployment and assessment of the performances, therefore of any possibility to remove some innermost biases of the underlying forecasting model.

In terms of contributions of our study, we have proved that different modeling assumptions can be pursued. If the aim is to simply resort to the centroid configurations, the standard techniques (PCA and K-Means) presented in literature are enough for it. However, if the task is extended to a fine-grained quantification, it is essential to switch the modeling paradigm to a probabilistic one. The overall global results remain inline with some references in literature, however it is interesting to derive some secondary knowledge such as the evolution of the patterns, and the statistical properties of the distributions matching some expected physical assumptions. Resorting to the approximation power of neural networks have given us more flexibility, drastically reducing the dimensionality of the feature space, while improving the separation of data points. The overall interpretability is enhanced too, given the optimization process leading to disentangled representations of the attributes. Thereby, the adoption of Mixture Models has led to a major robustness of the framework, as well as to an improved consistency of the clustering assignments.

Along this line, future works should then focus on some experimental and critical points we have encountered during the process.
Firstly, the adoption of VAEs for the dimensionality reduction step could be helpful to consider several snapshots of different atmospheric levels. Indeed, differently than PCA, Variational AutoEncoders can receive as input multiple-channels images, over which to perform the encoding step. In this context, instead of feeding a single anomaly map of the Geopotential at 500hPa \parencite{van_der_Wiel_2019,2011ClDy...36...19C,grams, article}, we could think to aggregate multiple pressure levels such as 700/850 hPa \parencite{Vautard1988, WR700hPa, article}, or sea level pressure \parencite{meteofrance, article}, thus better characterizing the datapoints and overcoming any strict choice in terms of which weather variable to consider.\\
Further, as the results on the probabilistic models show, a slight difference was spotted on the expected frequencies for AR and NAO- regimes. Whether this is a bias of the models, or an evidence of more faithful results has to be investigated. Then, other probabilistic modeling choices could be pursued \parencite{https://doi.org/10.1002/2016RG000538}, possibly leading to major performances.\\
On the quantification side, on the hand the limited data availability on the true measurements, on the other hand the sometimes misaligned nature of the synthetic data, represent two key limiting factors. In our experiments, we resort to techniques like quantile-quantile (QQ) mapping to ``re-align'' the synthetic data distribution to the true observation, however with poor results. Some efforts on this side could then be productive for a still more faithful analysis.\\
Finally, the forecasting tool we develop, as we mention in Chapter \ref{chap:forecasts}, is largely dependent on the precision of the underlying product from ECMWF. Surely, this represents the step with possibilities of larger improvement. Having access to raw forecasts of geopotential maps would represent the best possible scenario, ensuring the consistency with all the methods developed inside the pipeline. Further, it would allow to test several clusters conformation, differing by the number of regimes adopted, not mandatorily sticking with the theoretical ones. Alternatively, spotting some innermost biases the ECMWF model has, would translate into accentuating some longer-term signals, esepcially when they are uniformly mixed between each other. To accomplish this, however, several years of data should be necessary, thus not representing a feasible short-term solution.


